Suppose that you have a parcel of land for sale, and you receive offers of \(X_{t}\) at each time \(t \in[0, T)\), where \(\left(X_{t}\right)\) is a standard Brownian motion with initial state \(x\). At time \(T\) the game runs out and all offers are withdrawn. Consider a policy that exercises the option at the first time the offer exceeds a value \(y\), and does not accept an offer otherwise. Find an expression for the expected profit under such a policy as a function of \(y\). If \(T=10, x=100\), use Mathematica to find the optimal value of \(y\). (Hint: Express the event of earning a positive profit in terms of the maximum over times in \([0, T]\) of the Brownian motion \(X_{t}\), and use the result of Exercise 7 regarding the distribution of the maximum.)